Decision Support Puzzles for Applied Mathematicians
February 2009 - Supply & Demand
Moving resources efficiently from supplier to consumer is a challenging problem that can be solved using O.R. techniques. Figure 1 shows a map of blue factories that supply food to orange towns. The numbers below the factories and towns indicate how much food (in kg) each supplies and demands, respectively. Any factory can supply any amount of food to one or several towns. A new factory is being built that can supply 1,000 kg of food but the location of the factory has not yet been determined. The distance between adjacent cells on the map is 1 km. The cost to transport 1 kg of food 1 km is $10. The new factory cannot occupy a cell that already contains an existing factory or town.
Question: If the new factory is optimally located, what is the total transportation cost to satisfy the demand of all towns?